Aspects of Nuclear Physics: A joint meeting on QCD and QGP, (HADRON-RANP (original) (raw)
Pion masses at finite temperature
We present preliminary results on a study about the thermal variation of the charged and neutral pion masses to one loop, analyzing their electromagnetic difference, in the context of Chiral Perturbation Theory with two flavours, as well as using a light resonance model. We find that the pion mass difference increases for, at least, low and intermediate temperatures, unlike the chiral limit decreasing result. The axial-vector mixing arising from chiral restoration smooths the Debye-screening temperature increase. Taking into account further corrections due to axial and vector resonances, dominated by a 1 and ρ particles respectively, does not change significantly the ChPT prediction.
Two perspectives for the thermal behavior of an effective hadronic coupling constant
Nuclear Physics B - Proceedings Supplements, 1999
The pion nucleon vertex function at finite temperature is studied in two frameworks: (a) the thermal (linear) sigma model to leading (one-loop) order, and (b) a thermal QCD-Finite Energy Sum Rule. Both approaches indicate that the strength of the pion-nucleon coupling decreases with increasing T, vanishing at a critical temperature. The associated mean-square radius is a monot.onically increasing function of T. diverging at, t,he critical temperature. We interpret. this fact. as (analytical) evidence for deconfinement.
On pion mass and decay constant from theory
Europhysics Letters, 2021
We calculate the pion mass from Goldstone modes in the Higgs mechanism related to the neutron decay. The Goldstone pion modes acquire mass by a vacuum misalignment of the Higgs field. The size of the misalignment is controlled by the ratio between the electronic and the nucleonic energy scales. The nucleonic energy scale is involved in the neutron to proton transformation and the electronic scale is involved in the related creation of the electronic state in the course of the electroweak neutron decay. The respective scales influence the mapping of the intrinsic configuration spaces used in our description. The configuration spaces are the Lie groups U(3) for the nucleonic sector and U(2) for the electronic sector. These spaces are both compact and lead to periodic potentials in the Hamiltonians in coordinate space. The periodicity and strengths of these potentials control the vacuum misalignment and lead to a pion mass of 135.2(1.5) MeV with an uncertainty mainly from the fine stru...
Nucleon Properties at Finite Temperature in the Extended Quark-Sigma Model
American Journal of Physics and Applications, 2014
Hadron properties are studied at hot medium using the quark sigma model. The quark sigma model is extended to include eighth-order of mesonic interactions based on some aspects of quantum chromodynamic (QCD) theory. The extended effective potential tends to the original effective potential when the coupling between the higher order mesonic interactions equal to zero. The field equations have been solved in the mean-field approximation by using the extended iteration method. We found that the nucleon mass increases with increasing temperature and the magnetic moments of proton and neutron increase with increasing temperature. A comparison is presented with recent previous works and other models. We conclude that higher-order mesonic interactions play an important role in changing the behavior of nucleon properties at finite temperature. In addition, the deconfinement phase transition is satisfied in the present model.
The pion nucleon sigma term with dynamical Wilson fermions a feasibility study
Nuclear Physics B - Proceedings Supplements, 1997
We calculate connected and disconnected contributions to the flavour singlet scalar density amplitude of the nucleon in a full QCD lattice simulation with n f = 2 dynamical Wilson fermions at β = 5.6 on a 16 3 × 32 lattice. We find that both contributions are of similar size at the light quark mass. We arrive at the estimate σ πN = 18(5)MeV. Its smallness is directly related to the apparent decrease of u, d quark masses when unquenching QCD lattice simulations. The y parameter can be estimated from a semi-quenched analysis, in which there are no strange quarks in the sea, the result being y = 0.59(13).
QCD determination of the pion nucleon σ term and the strangeness content of the proton
Nuclear Physics B - Proceedings Supplements, 1991
A strong violation of the Quark Line Rule is observed if we allow the pion nucleon a term to attain the present experimental value. This in turn indicates the possibility of a large strangeness content in the proton. In this work we have shown that the value of the o term is seen to be raised from what is expected from the GMOR scheme of chiral symmetry breaking through a ~um~rule which shows that the ratio of the meson wave function renormalization constants Z-=/Z ~ may deviate considerably from unity by using the recent QCD estimate on the quark vacuum w-condensate ratio o/ ° I.
Australian Journal of Physics, 1998
The often used Gell-Mann-Oakes-Renner (GMOR) mass formula for Nambu-Goldstone bosons in QCD, such as the pions, involves the condensate < qq >, f π and the quark current masses. Within the context of the Global Colour Model (GCM) for QCD a manifestly different formula was recently found by Cahill and Gunner. Remarkably Langfeld and Kettner have shown the two formulae to be equivalent. Here we explain that the above recent analyses refer to the GCM constituent pion and not the exact GCM pion. Further, we suggest that the GMOR formula is generic. We generalise the Langfeld-Kettner identity to include the full response of the constituent quark propagators to the presence of a non-zero (and running) quark current mass.
Pion propagation in the linear sigma model at finite temperature
Physical Review D, 2000
We construct effective one-loop vertices and propagators in the linear sigma model at finite temperature, satisfying the chiral Ward identities and thus respecting chiral symmetry, treating the pion momentum, pion mass and temperature as small compared to the sigma mass. We use these objects to compute the two-loop pion self-energy. We find that the perturbative behavior of physical quantities, such as the temperature dependence of the pion mass, is well defined in this kinematical regime in terms of the parameter m 2 π /4π 2 f 2 π and show that an expansion in terms of this reproduces the dispersion curve obtained by means of chiral perturbation theory at leading order. The temperature dependence of the pion mass is such that the first and second order corrections in the above parameter have the same sign. We also study pion damping both in the elastic and inelastic channels to this order and compute the mean free path and mean collision time for a pion traveling in the medium before forming a sigma resonance and find a very good agreement with the result from chiral perturbation theory when using a value for the sigma mass of 600 MeV.
Electromagnetic effects in the pion dispersion relation at finite temperature
Physical Review D, 2014
We investigate the charged-neutral difference in the pion self-energy at finite temperature T . Within Chiral Perturbation Theory (ChPT) we extend a previous analysis performed in the chiral and soft pion limits. Our analysis with physical pion masses leads to additional non-negligible contributions for temperatures typical of a meson gas, including a momentum-dependent function for the self energy. In addition, a nonzero imaginary part arises to leading order, which we define consistently in the Coulomb gauge and comes from an infrared enhanced contribution due to thermal bath photons. For distributions typical of a heavy-ion meson gas, the charged and neutral pion masses and their difference depend on temperature through slowly increasing functions. Chiral symmetry restoration turns out to be ultimately responsible for keeping the charged-neutral mass difference smooth and compatible with the observed charged and neutral pion spectra. We study also phenomenological effects related to the thermal electromagnetic damping, which gives rise to corrections for transport coefficients and distinguishes between neutral and charged mean free times. An important part of the analysis is the connection with chiral symmetry restoration through the relation of the pion mass difference with the vector-axial spectral function difference, which holds at T = 0 due to a sum rule in the chiral and soft pion limits. We analyze the modifications of that sum rule including nonzero pion masses and temperature, up to O(T 2 ) ∼ O(M 2 π ). Both effects produce terms making the pion mass difference grow against chiral-restoring decreasing contributions. Finally, we analyze the corrections to the previous ChPT and sum rule results within the resonance saturation framework at finite temperature, including explicitly ρ and a1 exchanges. Our results show that the ChPT result is robust at low and intermediate temperatures, the leading resonance corrections within this framework being O(T 2 M 2 π /M 2 R ) with MR the involved resonance masses.
Pions at finite temperature from QCD sum rules
Physics Letters B, 1996
The temperature corrections to the current algebra Gell-Mann, Oakes, and Renner (GMOR) relation in SU (2) ⊗ SU (2) are investigated in the framework of QCD sum rules. There are no corrections at leading order in the quark masses. At the next to leading order we find corrections of the form m 2 q T 2 , which are small except near the critical temperature. As a by-product we obtain the temperature behaviour of the pion mass, which is essentially constant, except near the critical temperature where it increases with T .
Proceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022), 2022
We investigate the properties of the pion quasiparticle in the thermal hadronic phase of (2 + 1)-flavor QCD on the lattice at physical quark masses at a temperature = 128 MeV. We find that the pion quasiparticle mass 0 = 113(3) MeV is significantly reduced relative to the zero-temperature pion mass 0 = 128(1) MeV, by contrast with the static screening mass = 144(3) MeV, which increases with temperature. On the other hand the pion quasiparticle decay constant does not change much compared to the corresponding zero-temperature decay constant. The difference of the vector-and axialvector spectral functions serves as an order parameter of chiral symmetry restoration. By analyzing this quantity we conclude that chiral symmetry restoration is already at an advanced stage in the spectral function.
The ϱ meson and the thermal behavior of an effective hadronic coupling constant
Nuclear Physics B - Proceedings Supplements, 1998
Vector Meson Dominance ideas together with a Finite Energy QCD sum rule allows for the determination of the q 2 -and the T -dependence of the effective hadronic coupling constant gρππ in the space-like region. It turns out that gρππ(q 2 , T ) vanishes at the critical temperature Tc, independently of q 2 . A comparison with a previous independent QCD determination of the electromagnetic pion form factor at finite temperature supports the validity of Vector Meson Dominance at finite temperature. We find also thet the pion radius increases with T , having a divergent behavior at Tc.
Applicability of perturbative QCD and NLO power corrections for the pion form factor
Physical Review D, 2002
In many years ago, Isgur and Llewellyn Smith addressed that PQCD is inapplicable to exclusive processes , such as the pion form factor. The main problem is that the asymptotic of PQCD is only about one fourth of the experimental value . We reexamine this PQCD deep problem. By including NLO power corrections to the pion form factor, we may arrive at a perturbative explanation for the data. The key realization is that we need to interprete that the strong interaction coupling constant involved in the PQCD result should be taken as an effective coupling constant under nonperturbative QCD vaccum. This implies that one can equally identify the relevant scale for the effective coupling constant as the factorization scale about 1 GeV. We also find that the average momentum fraction variable locates about 0.5, which is in favor of the asymptotic pion wave function. By employing photon-pion form factor with NLO power corrections to factorize out the nonperturbative effects involved in the effective coupling constant, we can extract an effective running coupling constant, which represents an effective coupling involving in the hard scattering subprocesses. The difference between the effective running coupling constant and the usual perturbative running coupling constant (Λ QCD = 0.3 GeV) is very small for Q 2 > 1 GeV 2 . The effective running coupling constant αs/π is smaller than 0.2 for Q 2 > 1 GeV 2 . This directly showes that PQCD is applicable to exclusive processes at energy Q 2 > 1 GeV 2 . In summary, with NLO power corrections, PQCD can completely explain the Q 2 spectrum of pion form factor.
Influence of pions on the hadron-quark phase transition
2013
In this work we present the features of the hadron-quark phase transition diagrams in which the pions are included in the system. To construct such diagrams we use two different models in the description of the hadronic and quark sectors. At the quark level, we consider two distinct parametrizations of the Polyakov-Nambu-Jona-Lasinio (PNJL) models. In the hadronic side, we use a well known relativistic mean-field (RMF) nonlinear Walecka model. We show that the effect of the pions on the hadron-quark phase diagrams is to move the critical end point (CEP) of the transitions lines. Such an effect also depends on the value of the critical temperature (T 0) in the pure gauge sector used to parametrize the PNJL models. Here we treat the phase transitions using two values for T 0 , namely, T 0 = 270 MeV and T 0 = 190 MeV. The last value is used to reproduce lattice QCD data for the transition temperature at zero chemical potential.
Pion decays and the pion electromagnetic form factor in a σ-model with quarks
Nuclear Physics B, 1978
We study in the one-loop approximation the decays of the pion and the pion electromagnetic form factor at low q2 in the framework of a a-model with quarks. The theory has a free parameters the quark and o masses and the results are very insensitive to their values. We get good approximation for all processes considered except for the ratio of the axial to the vector form factor that appear in the electronic radiative decay of the charged pion. The reason is probably that our model includes the pion-pion interaction only in the isoscalar s-wave at the one-loop level.
Determination of the Pion Charge Form Factor at Q^{2}=1.60 and 2.45 (GeV/c)^{2}
Physical Review Letters, 2006
The 1 H(e, e ′ π + )n cross section was measured at four-momentum transfers of Q 2 =1.60 and 2.45 GeV 2 at an invariant mass of the photon nucleon system of W =2.22 GeV. The charged pion form factor (Fπ) was extracted from the data by comparing the separated longitudinal pion electroproduction cross section to a Regge model prediction in which Fπ is a free parameter. The results indicate that the pion form factor deviates from the charge-radius constrained monopole form at these values of Q 2 by one sigma, but is still far from its perturbative Quantum Chromo-Dynamics prediction.
Fate of pion condensation in quark matter: From the chiral limit to the physical pion mass
Physical Review D, 2009
We study aspects of the pion condensation in two-flavor neutral quark matter using the Nambu-Jona-Lasinio model of QCD at finite density. We investigate the role of electric charge neutrality, and explicit symmetry breaking via quark mass, both of which control the onset of the charged pion (π c ) condensation. We show that the equality between the electric chemical potential and the in-medium pion mass, µe = M π − , as a threshold, persists even for a composite pion system in the medium, provided the transition to the pion condensed phase is of the second order. Moreover, we find that the pion condensate in neutral quark matter is extremely fragile to the symmetry breaking effect via a current quark mass m, and is ruled out for m larger than the order of 10 keV.
Pion Interactions and the Standard Model at High Precision
arXiv: History and Philosophy of Physics, 2018
Pions were predicted by H. Yukawa as force carriers of the inter-nucleon forces, and were detected in 1947. Today they are known to be bound states of quarks and anti-quarks of the two lightest flavours. They satisfy Bose statistics, and are the lightest particles of the strong interaction spectrum. Determination of the parameters of the Standard Model, including the masses of the lightest quarks, has only recently reached high precision on the lattice. Pions are also known to be pseudo-Goldstone bosons of spontaneously broken approximate axial-vector symmetries, and a probe of their properties and interactions at high precision tests our knowledge of the strong interactions. While also being a probe of the solution of the strong interactions on the computer, which is known as lattice gauge theory. Despite their long history, there are significant experimental and theoretical challenges in determining their properties at high precision. Examples include the lifetime of the neutral p...